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Simplifying 0 = 2m2 + -1m + -12 Reorder the terms: 0 = -12 + -1m + 2m2 Solving 0 = -12 + -1m + 2m2 Solving for variable 'm'. Combine like terms: 0 + 12 = 12 12 + m + -2m2 = -12 + -1m + 2m2 + 12 + m + -2m2 Reorder the terms: 12 + m + -2m2 = -12 + 12 + -1m + m + 2m2 + -2m2 Combine like terms: -12 + 12 = 0 12 + m + -2m2 = 0 + -1m + m + 2m2 + -2m2 12 + m + -2m2 = -1m + m + 2m2 + -2m2 Combine like terms: -1m + m = 0 12 + m + -2m2 = 0 + 2m2 + -2m2 12 + m + -2m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 12 + m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -0.5m + m2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.5m + 6 + m2 = 0 + 6 Reorder the terms: -6 + 6 + -0.5m + m2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.5m + m2 = 0 + 6 -0.5m + m2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.5m + m2 = 6 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.5m + 0.25 + m2 = 6 + 0.25 Reorder the terms: 0.25 + -0.5m + m2 = 6 + 0.25 Combine like terms: 6 + 0.25 = 6.25 0.25 + -0.5m + m2 = 6.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (m + 0.5) equal to 2.5 and -2.5.Subproblem 1
m + 0.5 = 2.5 Simplifying m + 0.5 = 2.5 Reorder the terms: 0.5 + m = 2.5 Solving 0.5 + m = 2.5 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 2.5 + -0.5 m = 2.5 + -0.5 Combine like terms: 2.5 + -0.5 = 2 m = 2 Simplifying m = 2Subproblem 2
m + 0.5 = -2.5 Simplifying m + 0.5 = -2.5 Reorder the terms: 0.5 + m = -2.5 Solving 0.5 + m = -2.5 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -2.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -2.5 + -0.5 m = -2.5 + -0.5 Combine like terms: -2.5 + -0.5 = -3 m = -3 Simplifying m = -3Solution
The solution to the problem is based on the solutions from the subproblems. m = {2, -3}
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